If many samples are taken from the same population, their means will be different.Question 7Select one:TrueFalse

Answer

The statement "If many samples are taken from the same population, their means will be different" is True.

When multiple samples are drawn from the same population, each sample can have a different mean due to natural sampling variability. This variability occurs even when sampling from the same population because different elements of the population may be included in different samples. This phenomenon is a key principle in statistics and underlines the concept of the sampling distribution of the sample mean, which illustrates that while the means of individual samples can differ, they will cluster around the population mean as the number of samples increases.

In a practical sense, if you were to randomly select samples of a fixed size from a large population (say, measuring the heights of a group of people), the average height calculated from each sample may vary due to the randomness of the selection, even though all samples come from the same overarching group.